My iPad Mini 32GB wifi only running on 6.0.1 had this issue too. I was troubleshooting and streamlined it to two issues.
First, I swapped out my existing router with an older one. No connectivity or speed issues.
Next, I tried a restore of my existing router to out of the box state, and connected my ipad mini to it, no connectivity issues at all. Full signal and full speed.
I discovered when the connection was good, the router was operating at Channel 2 (TP-Link TL-WR841ND). When I switched the channel to Auto (it randomly picked 1 and 6) and while it was operating on those channels, the iPad Mini had connectivity issues. Full signal but slow speeds.
For my case, I discovered that my iPad has incompatibilty issues with my existing router.
So I deduce that my iPad Mini doesn't have hardware issues.